The Sum Nobody Priced: Hartle and Hawking's Contour and Measure, Still Chosen
The no-boundary proposal says the universe's wave function is a path integral over compact Euclidean geometries that end on the three-geometry you are asking about, with no boundary at the other end. A sum needs two things before it is a sum: a route, and a weight for each thing summed. The 1983 paper derives neither. This paper counts what that costs. The route, the lapse contour, is one complex dial. The weight, the measure over geometries, is one real dial, and in minisuperspace it shows up as a single exponent p. A third dial of the same species, the factor ordering of the Wheeler-DeWitt operator, is counted here and not priced. Selection equations supplied by the paper for any of them: zero. Hold the wave function fixed and turn only the measure dial, and the proposal's own statistics walk: the mean scale factor moves from 0.564190 to 2.872939, a factor of 5.092, and the upper tail moves by a factor of 29.5. Pick the other classic contour and the weight at one test point changes by a factor of 8919.157, computed twice with independent code. The perturbation sign that decides whether the universe in the proposal is stable is not derived either; the wrong-sign side is not a distribution at all, and the sign in use was set by hand to the answer wanted. Two priced dials, one counted dial, zero selection equations. Verdict: a reason was found, and the question remains open (not solved).
Authors
- William Alexander Aldred
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-01
- DOI
- https://doi.org/10.5281/zenodo.23889658
- Primary Topic
- Cosmology and Gravitation Theories
- Type
- preprint